What is the answer to solvefor y, y/(e^{xy)}=x ?

The answer to solvefor y, y/(e^{xy)}=x is No Solution for y\in\mathbb{R}

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solvefor y, y/(e^{xy)}=x

solve for

y, \frac{y}{e ^{x y}} = x

No Solution for y \in R

Solution steps

\frac{y}{e ^{x y}} = x

Prepare

\frac{y}{e ^{x y}} = x

for Lambert form:

y e^{- x y} = x

Rewrite the equation with

- x y = u

and

y = - \frac{u}{x}

(- \frac{u}{x}) e^{u} = x

Rewrite

(- \frac{u}{x}) e^{u} = x

in Lambert form:

e^{u} u = - x^{2}

Solve

e^{u} u = - x^{2} : u = W (- x^{2})

u = W (- x^{2})

Substitute back

u = - x y,

solve for

y

Solve

- x y = W (- x^{2}) : y = - \frac{W ( - x ^{2} )}{x}

y = - \frac{W ( - x ^{2} )}{x}

Verify Solutions:

y = - \frac{W ( - x ^{2} )}{x}

False

The solution is

No Solution for y \in R

2^{5 x - 2} = 2^{x + 2}

2^{2 x + 7} = 2^{15}

3^{2 7^{x + 3}} = 2 7^{9^{x + 3}}

3^{2 x - 1} = 17

x, e^{7 - 4 x} = 6

What is the answer to solvefor y, y/(e^{xy)}=x ?
The answer to solvefor y, y/(e^{xy)}=x is No Solution for y\in\mathbb{R}